Machines referred to as demolition robots are remote-controlled working machines intended for different demolition operations, in which the operator walks beside the machine and controls its different movements. He does this using a remote control which he straps on so that it sits in front of his stomach at a suitable working height. The remote control has two control sticks and a series of different buttons and knobs. The machine is used in several different working modes. It is first moved up to the working surface, e.g. a wall, to be demolished. Its support legs are then lowered so that the machine stands steady. This is a set-up mode. The actual demolition work then begins in a work mode. So that it is possible to execute a plurality of different movements with only two control sticks, the control sticks are given different functions in the different working modes. In a known type of machine referred to as Brock, travel or transport is effected by pressing a button on each control stick. The machine then goes forwards or backwards at a fixed speed. The operator therefore has to use both hands and, in order to be able to turn, he has to change the work mode to a mode allowing for turning. As the machine is electrically driven, a power cable has to be connected to the mains and the machine thus trails the cable behind it during travel. One problem is that the power cable may become jammed under the machine or become entangled with an object in the vicinity. When this begins to happen, the operator has to let go of at least one control stick and therefore interrupt travel in order then to straighten the cable and continue travel. This is a slow and inefficient way of working. Furthermore, both hands are used for the travel operation so that he cannot simultaneously operate the rotating tower of the machine or any other part that has to be rotated during travel. Instead, travel also has to be interrupted in this case.